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Question
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
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Solution
Given that, `x= 2+sqrt3` hence
\[\frac{1}{x}\] is given as
. `1/x = 1/(2+sqrt3)`We are asked to find `x +1/x `
We know that rationalization factor for `2+sqrt3` is`2-sqrt3` . We will multiply each side of the given expression `1/(2+sqrt3)` by, `2-sqrt3` to get
. `1/x = 1/(2+sqrt3) xx(2-sqrt3)/(2-sqrt3)`
`= (2-sqrt3)/((2)^2-(sqrt3)^2)`
`= (2-sqrt3)/(4-3)`
`=2-sqrt3`
Therefore,
`x+1/x = 2+sqrt3 +2 - sqrt3`
`=4`
Hence value of the given expression is 4 .
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